Publication Information

{'id': 'https://openalex.org/W2791163049', 'doi': None, 'title': 'Fractional derivative of composite functions: exact results and physical applications', 'display_name': 'Fractional derivative of composite functions: exact results and physical applications', 'publication_year': 2018, 'publication_date': '2018-03-07', 'ids': {'openalex': 'https://openalex.org/W2791163049', 'mag': '2791163049'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'http://export.arxiv.org/pdf/1803.05018', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'type': 'preprint', 'type_crossref': 'posted-content', 'indexed_in': [], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5083178571', 'display_name': 'Gavriil Shchedrin', 'orcid': None}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Gavriil Shchedrin', 'raw_affiliation_strings': [], 'affiliations': []}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5013108292', 'display_name': 'Nathanael C. Smith', 'orcid': None}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Nathanael C. Smith', 'raw_affiliation_strings': [], 'affiliations': []}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5030457805', 'display_name': 'Anastasia Gladkina', 'orcid': None}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Anastasia Gladkina', 'raw_affiliation_strings': [], 'affiliations': []}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5085273013', 'display_name': 'Lincoln D. Carr', 'orcid': 'https://orcid.org/0000-0002-4848-7941'}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Lincoln D. Carr', 'raw_affiliation_strings': [], 'affiliations': []}], 'institution_assertions': [], 'countries_distinct_count': 0, 'institutions_distinct_count': 0, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': None, 'has_fulltext': False, 'cited_by_count': 3, 'citation_normalized_percentile': {'value': 0.759036, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 74, 'max': 77}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10288', 'display_name': 'Fractional Differential Equations Solutions', 'score': 0.9995, 'subfield': {'id': 'https://openalex.org/subfields/2611', 'display_name': 'Modeling and Simulation'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T10288', 'display_name': 'Fractional Differential Equations Solutions', 'score': 0.9995, 'subfield': {'id': 'https://openalex.org/subfields/2611', 'display_name': 'Modeling and Simulation'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10248', 'display_name': 'Nonlinear Waves and Solitons', 'score': 0.9872, 'subfield': {'id': 'https://openalex.org/subfields/3109', 'display_name': 'Statistical and Nonlinear Physics'}, 'field': {'id': 'https://openalex.org/fields/31', 'display_name': 'Physics and Astronomy'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10407', 'display_name': 'Lipid Membrane Structure and Behavior', 'score': 0.9791, 'subfield': {'id': 'https://openalex.org/subfields/1312', 'display_name': 'Molecular Biology'}, 'field': {'id': 'https://openalex.org/fields/13', 'display_name': 'Biochemistry, Genetics and Molecular Biology'}, 'domain': {'id': 'https://openalex.org/domains/1', 'display_name': 'Life Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/hypergeometric-distribution', 'display_name': 'Hypergeometric distribution', 'score': 0.4416709}, {'id': 'https://openalex.org/keywords/derivative', 'display_name': 'Derivative (finance)', 'score': 0.4301684}], 'concepts': [{'id': 'https://openalex.org/C154249771', 'wikidata': 'https://www.wikidata.org/wiki/Q1339058', 'display_name': 'Fractional calculus', 'level': 2, 'score': 0.8553622}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.6311419}, {'id': 'https://openalex.org/C197320386', 'wikidata': 'https://www.wikidata.org/wiki/Q21028472', 'display_name': 'Hypergeometric function', 'level': 2, 'score': 0.5952791}, {'id': 'https://openalex.org/C90673727', 'wikidata': 'https://www.wikidata.org/wiki/Q901718', 'display_name': 'Product (mathematics)', 'level': 2, 'score': 0.5182564}, {'id': 'https://openalex.org/C158241908', 'wikidata': 'https://www.wikidata.org/wiki/Q109744257', 'display_name': 'Generalized hypergeometric function', 'level': 3, 'score': 0.5090213}, {'id': 'https://openalex.org/C177148314', 'wikidata': 'https://www.wikidata.org/wiki/Q170084', 'display_name': 'Generalization', 'level': 2, 'score': 0.4742966}, {'id': 'https://openalex.org/C176671685', 'wikidata': 'https://www.wikidata.org/wiki/Q730600', 'display_name': 'Hypergeometric distribution', 'level': 2, 'score': 0.4416709}, {'id': 'https://openalex.org/C28826006', 'wikidata': 'https://www.wikidata.org/wiki/Q33521', 'display_name': 'Applied mathematics', 'level': 1, 'score': 0.43950582}, {'id': 'https://openalex.org/C148160416', 'wikidata': 'https://www.wikidata.org/wiki/Q783948', 'display_name': 'Confluent hypergeometric function', 'level': 3, 'score': 0.43482596}, {'id': 'https://openalex.org/C111771559', 'wikidata': 'https://www.wikidata.org/wiki/Q66295', 'display_name': 'Derivative (finance)', 'level': 2, 'score': 0.4301684}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.42129442}, {'id': 'https://openalex.org/C82240120', 'wikidata': 'https://www.wikidata.org/wiki/Q190573', 'display_name': 'Gamma function', 'level': 2, 'score': 0.41937298}, {'id': 'https://openalex.org/C143724316', 'wikidata': 'https://www.wikidata.org/wiki/Q312468', 'display_name': 'Series (stratigraphy)', 'level': 2, 'score': 0.41187578}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.3297329}, {'id': 'https://openalex.org/C151730666', 'wikidata': 'https://www.wikidata.org/wiki/Q7205', 'display_name': 'Paleontology', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C106159729', 'wikidata': 'https://www.wikidata.org/wiki/Q2294553', 'display_name': 'Financial economics', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C162324750', 'wikidata': 'https://www.wikidata.org/wiki/Q8134', 'display_name': 'Economics', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C86803240', 'wikidata': 'https://www.wikidata.org/wiki/Q420', 'display_name': 'Biology', 'level': 0, 'score': 0.0}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'http://export.arxiv.org/pdf/1803.05018', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 35, 'referenced_works': ['https://openalex.org/W1599013339', 'https://openalex.org/W171286733', 'https://openalex.org/W1966793822', 'https://openalex.org/W1968134101', 'https://openalex.org/W1973352373', 'https://openalex.org/W1975383112', 'https://openalex.org/W1982261380', 'https://openalex.org/W1993680495', 'https://openalex.org/W2011368105', 'https://openalex.org/W2016585644', 'https://openalex.org/W2018965660', 'https://openalex.org/W2023065763', 'https://openalex.org/W2023600694', 'https://openalex.org/W2045350842', 'https://openalex.org/W2045882715', 'https://openalex.org/W2046322851', 'https://openalex.org/W2057293894', 'https://openalex.org/W2058860728', 'https://openalex.org/W2062316858', 'https://openalex.org/W2070454382', 'https://openalex.org/W2080296395', 'https://openalex.org/W2080843536', 'https://openalex.org/W2095214881', 'https://openalex.org/W2108338926', 'https://openalex.org/W2111271983', 'https://openalex.org/W2115673781', 'https://openalex.org/W2122171697', 'https://openalex.org/W2130620182', 'https://openalex.org/W2152825691', 'https://openalex.org/W2314482512', 'https://openalex.org/W2316090223', 'https://openalex.org/W2605164388', 'https://openalex.org/W2765792601', 'https://openalex.org/W2768108854', 'https://openalex.org/W3150837077'], 'related_works': ['https://openalex.org/W3098134484', 'https://openalex.org/W3021529274', 'https://openalex.org/W2922924449', 'https://openalex.org/W2886835231', 'https://openalex.org/W2802275298', 'https://openalex.org/W2792080443', 'https://openalex.org/W2772995680', 'https://openalex.org/W2768108854', 'https://openalex.org/W2760840805', 'https://openalex.org/W2569333703', 'https://openalex.org/W2557239909', 'https://openalex.org/W2520410115', 'https://openalex.org/W2516758181', 'https://openalex.org/W2500614803', 'https://openalex.org/W2132085296', 'https://openalex.org/W2036420971', 'https://openalex.org/W1600950487', 'https://openalex.org/W1561293575', 'https://openalex.org/W1556035056', 'https://openalex.org/W111073650'], 'abstract_inverted_index': {'We': [0, 154, 180], 'examine': [1], 'the': [2, 13, 19, 69, 75, 82, 85, 102, 106, 112, 116, 120, 130, 140, 156, 160, 164, 177, 184, 200], 'fractional': [3, 21, 56, 77, 86, 107, 166, 189], 'derivative': [4, 57, 78, 87, 167], 'of': [5, 12, 46, 58, 65, 74, 84, 90, 94, 105, 115, 119, 145, 150, 163, 168, 199], 'composite': [6], 'functions': [7], 'and': [8, 15, 30, 37, 44, 71, 191], 'present': [9], 'a': [10, 55, 125, 146, 151], 'generalization': [11], 'product': [14, 70, 108, 192], 'chain': [16, 72, 190], 'rules': [17, 73, 193], 'for': [18, 28], 'Caputo': [20, 76, 165], 'derivative.': [22], 'These': [23], 'results': [24, 158], 'are': [25, 52, 79, 136], 'especially': [26], 'important': [27], 'physical': [29], 'biological': [31], 'systems': [32], 'that': [33, 182], 'exhibit': [34], 'multiple': [35], 'spatial': [36], 'temporal': [38], 'scales,': [39], 'such': [40], 'as': [41], 'porous': [42], 'materials': [43], 'clusters': [45], 'neurons,': [47], 'in': [48, 63, 88, 101, 143, 176, 183, 195], 'which': [49, 171], 'transport': [50], 'phenomena': [51], 'governed': [53], 'by': [54, 159], 'slowly': [59], 'varying': [60], 'parameters': [61], 'given': [62], 'terms': [64, 89, 144], 'elementary': [66], 'functions.': [67, 203], 'Both': [68], 'obtained': [80, 157], 'from': [81], 'expansion': [83], 'an': [91, 196], 'infinite': [92, 197], 'series': [93, 198], 'integer': [95], 'order': [96], 'derivatives.': [97], 'The': [98], 'crucial': [99], 'step': [100], 'practical': [103], 'implementation': [104], 'rule': [109], 'relies': [110], 'on': [111], 'exact': [113, 161], 'evaluation': [114, 162], 'repeated': [117, 141], 'integral': [118, 133, 142], 'generalized': [121, 131, 201], 'hypergeometric': [122, 148, 202], 'function': [123, 149], 'with': [124], 'power-law': [126], 'argument.': [127], 'By': [128], 'applying': [129], "Euler's": [132], 'transform,': [134], 'we': [135], 'able': [137], 'to': [138], 'represent': [139], 'single': [147], 'higher': [152], 'order.': [153], 'demonstrate': [155], 'hyperbolic': [169], 'tangent': [170], 'describes': [172], 'dark': [173], 'soliton': [174], 'propagation': [175], 'non-linear': [178], 'media.': [179], 'conclude': [181], 'most': [185], 'general': [186], 'case': [187], 'both': [188], 'result': [194]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2791163049', 'counts_by_year': [{'year': 2020, 'cited_by_count': 2}, {'year': 2019, 'cited_by_count': 1}], 'updated_date': '2024-12-12T10:17:14.678714', 'created_date': '2018-03-29'}